Carrie and Larry must divide a xylophone, a yoyo, and a zebra. (All items are divisible.) They assign points to each item as follows: Carrie: xylophone 70, yoyo 20, zebra 10. Larry: xylophone 50, yoyo 30, zebra 20. They divide the items according to the adjusted winner procedure. Assuming that Larry tells the truth, can Carrie get a better outcome for herself by lying about her point values?

a. Yes, by reporting xylophone 40, yoyo 35, zebra 25
b. Yes, by reporting xylophone 100, yoyo zebra 0.
c. Yes, by reporting xylophone 60, yoyo 25, zebra 15
d. No.
e. Yes, by reporting xylophone 0, yoyo 0, zebra 100

Answer / Explanation

To properly answer this question, let us first understand what the adjusted winner procedure is:

The adjusted winner procedure is a method for dividing assets between two individuals especially in the aspects of couples. It requires each person to divide 100 points among the assets which will reflect their relative values of the items.

It also requires that the assets be divisible.

Each item is then tentatively assigned to the party which placed more points on that item or asset.

The person who has a lower point total then acquires from the other the part of the asset for which the ratio of the recipient's point assignment to the donor's point assignment is highest (this ratio will be less than one, since the donor has the item because she valued it more).

The amount of the asset that is transferred is determined so that after it is transferred, the point totals of the two parties will be equal.

This particular type of process is rift free and it is good to know that no other division could increase the satisfaction of both parties.

Now referring back to the narrate of the question asked, The answer is b. yes, by reporting Xylophone 100, yoyo zebra 0 Carrie can get a better outcome for herself by lying about her point values.

(e)Yes, by reporting xylophone 0, yoyo 0, zebra 100.

Explanation:

Carrie get better outcome lying about her point values by reporting xylophone 0, yoyo 0, zebra 100.

Doing this, Larry saying the truth will get xylophone (50) and Yoyo(30). Total of 80

Carrie lying will be getting zebra(100). Total of 100

With this lies, Carie will get get better point for herself.

Properties of adjusted winners procedure are:

Envy-freeness: Each agent believes that his share of the goods is at least as good as the other share;

Equitability: The "relative happiness levels" of both agents from their shares are equal;

Pareto-optimality: no other allocation is better for one agent and at least as good for the other agent;

Proportionate: At most one good has to be divided between the agents.